For a model system consisting of a ferromagnetic layer coupled to a diluted, antiferromagnetic layer extensive Monte Carlo simulations are performed. Exchange bias is observed as a result of a domain state in the antiferromagnetic layer which develops during field cooling, carrying an irreversible domain state s magnetization. In agreement with recent experimental observations on Co/CoO bilayers a strong dependence of the exchange bias field on dilution of the antiferromagnet is found and it is shown that a variety of typical effects associated with exchange bias, such as positive bias, temperature, and time dependencies as well as the dependence on the thickness of the antiferromagnetic layer can be explained within our model.